A293866 For n > 2: when computing A229037(n), there are up to floor((n-1)/2) forbidden values (i.e. values that would lead to an arithmetic progression); a(n) = greatest forbidden value when computing A229037(n).

1, 3, 3, 1, 3, 3, 6, 6, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 11, 11, 12, 13, 14, 12, 13, 14, 14, 15, 16, 14, 15, 16, 16, 17, 17, 16, 17, 17, 14, 15, 16, 16, 17, 17, 16, 17, 17, 12, 13, 14, 13, 13, 14, 14, 15, 16, 16, 16, 16, 18, 17, 24, 17, 21, 21, 18, 21

Offset

3,2

Comments

The scatterplot of this sequence has interesting features, such as rectangular clusters of points.

For any n > 2, A229037(n) <= a(n) + 1, with equality for n=3, 6, 8, 24 (and possibly no other values).

Links

Rémy Sigrist, Table of n, a(n) for n = 3..10000

Rémy Sigrist, Scatterplot of the first 100000 terms

Rémy Sigrist, C++ program for A293866

Formula

a(n) = max_{j=1..floor((n-1)/2)} (2*A229037(n-j) - A229037(n-2*j)).

Example

For n=7: A229037(7) must be distinct from:
- 2*A229037(7-1) - A229037(7-2) = 2*2 - 1 = 3,
- 2*A229037(7-2) - A229037(7-4) = 2*1 - 2 = 2,
- 2*A229037(7-3) - A229037(7-6) = 2*1 - 1 = 1.
Hence a(7) = 3.

Prog

(C++) See Links section.

Crossrefs

Cf. A229037.

Sequence in context: A125562 A337910 A092040 * A161200 A214747 A110766

Adjacent sequences: A293863 A293864 A293865 * A293867 A293868 A293869

Keyword

nonn,look

Author

Rémy Sigrist, Oct 18 2017

Status

approved